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A comprehensive, structured reference to master computer science fundamentals, data structures, and algorithmic techniques from beginner level to advanced product-company interview standards.
Big-O quantifies upper-bound growth rates relative to input size N. Below is the essential complexity hierarchy:
| Notation | Name | Growth Rate | Max N (1 sec) | Typical Operations |
|---|---|---|---|---|
O(1) |
Constant | Flat | โ | Array index access, Hash Map fetch, Stack push/pop |
O(log N) |
Logarithmic | Extremely Slow | 10ยนโธ | Binary search, Balanced BST lookup, Euclidean GCD |
O(N) |
Linear | Proportional | 10โท | Single array loop, Hash Map building, BFS/DFS traversal |
O(N log N) |
Linearithmic | Moderate | 10โถ | Merge Sort, QuickSort average, HeapSort, Priority Queue operations |
O(Nยฒ) |
Quadratic | Fast Growth | 10โด | Nested loops, Bubble/Insertion Sort, All-pairs distance grid |
O(2โฟ) |
Exponential | Explosive | 20 | Generating all subsets, Naive Fibonacci recursion |
O(N!) |
Factorial | Extreme | 10 | Generating all permutations, Traveling Salesperson brute force |
Contiguous memory allocations enabling O(1) index lookups. Master Two Pointers and Sliding Window subsegment mechanics.
O(N) Sorted Pair Sums.P[i] = P[i-1] + A[i] for O(1) range queries.Key-value mappings translating keys to bucket indices. Delivers average O(1) insertions, lookups, and deletions.
O(1) cache evicted updates.Node pointers allocating data dynamically without requirement for contiguous memory blocks.
prev, curr, next.Linear structures enforcing strict LIFO (Last-In-First-Out) and FIFO (First-In-First-Out) access mechanics.
O(N).O(1) push/pop at both ends for Sliding Window Maximum.Divide-and-conquer search algorithm halving search space at each iteration (O(log N)).
Ordering elements according to relational criteria. Inplace vs Stable sorting algorithms.
O(N log N) time and O(N) space.O(N log N) time.Hierarchical tree node structures. Binary Search Trees satisfy Left < Root < Right invariant.
Complete binary trees maintaining Min-Heap or Max-Heap property stored efficiently in arrays.
O(N log K) processing.Tree structure designed for character prefix lookup. Delivers O(Length) word operations.
Representations via Adjacency Lists/Matrices modeling networks, components, and weighted distances.
O(ฮฑ(N)) connectivity.Task dependency resolution and subproblem caching optimization.
Decision-tree search and fast bitwise binary computations.
x ^ x = 0 and x ^ 0 = x for single number discovery.O(log N) modular power calculation.Track your overall progress, difficulty distribution, streak history, and smart recommendations.